To determine whether each relation is a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). If any input is associated with more than one output, the relation is
not a function.
Let's analyze each problem step by step:
---
Problem 1:
| x | y |
|---|---|
| 5 | 1 |
| 5 | 2 |
| 5 | 3 |
| 5 | 4 |
- The input \( x = 5 \) is associated with multiple outputs: 1, 2, 3, and 4.
-
Conclusion: This is
not a function.
---
Problem 2:
- Input: \( 6, 8, 11, 14 \)
- Output: \( 9, 11, 15, 20 \)
- Each input is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 3:
- Input: \( -5, -2, 1, 0 \)
- Output: \( 2, 8, 7, 6 \)
- Each input is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 4:
- Points: \( (-9, 4), (2, 8), (0, 1), (6, 5), (2, 3) \)
- The input \( x = 2 \) is associated with two outputs: 8 and 3.
-
Conclusion: This is
not a function.
---
Problem 5:
| x | 6 | 8 | 10 | 12 | 14 |
|---|---|---|----|----|----|
| y | -4 | 2 | 6 | -4 | 11 |
- Each input is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 6:
- Input: \( 3, 6, 9, 12 \)
- Output: \( 2, 4, 6 \)
- Each input is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 7:
- Points: \( (-11, 14), (-13, 14), (3, 12), (1, 14), (8, 11) \)
- Each input is associated with exactly one output.
-
Conclusion: This is a function.
---
Problem 8:
| x | y |
|---|---|
| -9 | 4 |
| -8 | 3 |
| -8 | 1 |
| -6 | 0 |
| -4 | -3 |
- The input \( x = -8 \) is associated with two outputs: 3 and 1.
-
Conclusion: This is
not a function.
---
Final Answers:
1. Not a function
2. Function
3. Function
4. Not a function
5. Function
6. Function
7. Function
8. Not a function
\[
\boxed{\text{Not a function, Function, Function, Not a function, Function, Function, Function, Not a function}}
\]
Parent Tip: Review the logic above to help your child master the concept of function or not a function worksheet.
